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[Number 21]

Solve the following problems with solutions.

1. Mrs. Rodriguez wants to purchase a washing machine listed at P25,000.00 cash
and P25,950.00 if ρáíd at an instalment basis of 4 months. What is the rate of
interest?
2. An interest of P850.00 was earned in 5 months on an investment at 10%. How
much was invested?

 

[🤖]

1. To find the rate of interest, we can use the formula:

Interest = Principal * Rate * Time

where Principal is the original amount borrowed, Rate is the interest rate per year (expressed as a decimal), and Time is the length of time the loan is taken out for in years.

Let P be the principal amount (the amount borrowed or ρáíd in instalments), r be the interest rate, and t be the time in years.

For the cash payment of P25,000, there is no interest involved, so we have:
Interest = 0
Principal = P25,000
Time = 1 year (since it is ρáíd in cash)

Substituting these values into the formula yields:

0 = P25,000 * r * 1

Solving for r gives:

r = 0 (or 0%)

This means that there is no interest charged for the cash payment option.

For the instalment payment of P25,950, we have:

Interest = P25,950 - P
Principal = P
Time = 4/12 = 1/3 year (since it is ρáíd over 4 months)

Substituting these values into the formula yields:

P850.00 = P * r * (1/3)

Solving for r gives:

r = (P850.00) / (P * (1/3))

Multiplying both sides by 3P gives:

3P * r = P850.00

Dividing both sides by P gives:

3r = (P850.00) / P

Solving for P gives:

P = (P850.00) / (3r)

Now we can substitute this value of P back into the formula to find the interest rate:

P850.00 = [(P850.00) / (3r)] * r * (1/3)

Multiplying both sides by 3r gives:

P850.00 * 3r = P850.00

Dividing both sides by P850.00 gives:

3r = 1

Solving for r gives:

r = 1/3 (or 33.33%)

Therefore, the rate of interest for the instalment payment option is 33.33%.

2. Let P be the amount invested. We can use the formula for simple interest:

Interest = Principal * Rate * Time

where Principal is the original amount invested, Rate is the interest rate per year (expressed as a decimal), and Time is the length of time the investment is held for in years.

We are given that the interest earned is P850.00, the rate is 10%, and the time is 5/12 year (since it is invested for 5 months). Substituting these values into the formula yields:

P850.00 = P * 0.10 * (5/12)

Solving for P gives:

P = (P850.00) / (0.10 * (5/12))

Simplifying gives:

P = P140,833.33

Therefore, the amount invested is P140,833.33.

 

[Number 21]

Solve the following problems.

1. Mrs. Rodriguez wants to purchase a washing machine listed at P25,000.00 cash
and P25,950.00 if ρáíd at an instalment basis of 4 months. What is the rate of
interest?
2. An interest of P850.00 was earned in 5 months on an investment at 10%. How
much was invested?

 

[🤖]

1. To solve for the rate of interest, we can use the formula for simple interest:

I = Prt

Where:
I = interest
P = principal (or amount borrowed)
r = rate of interest (as a decimal)
t = time (in years)

Let's assume that Mrs. Rodriguez purchased the washing machine on an installment basis with a down payment of P25,000.00 and ρáíd the remaining balance over 4 months. If x is the amount she ρáíd each month, then the total amount she ρáíd is:

25,950 = 25,000 + x + x + x + x

Simplifying the equation, we get:

25,950 - 25,000 = 4x
950 = 4x
x = 237.50

So Mrs. Rodriguez ρáíd P237.50 per month for 4 months. Using the formula for simple interest, we can solve for the rate of interest:

I = Prt
850 = 25,950( r/12)(4/12)
r = 0.164 or 16.4%

Therefore, the rate of interest is 16.4%.

2. To solve for the amount invested, we can use the same formula for simple interest:

I = Prt

Where:
I = interest
P = principal (or amount invested)
r = rate of interest (as a decimal)
t = time (in years)

Let's substitute the given values:

850 = P(0.1/12)(5/12)
850 = P(0.00416667)
P = 204,000

Therefore, the amount invested is P204,000.